Light emitting diodes (LEDs) are used as sources of light for a variety of applications. For example, LEDs may be used as white light sources in various applications, such as flash sources for cellular telephone cameras and filament lamps. Such LEDs may be referred to herein as white LEDs or white-appearing LEDs. White LEDs may appear to emit white light from the perspective of the viewer when the LEDs are in an on state. In some cases, the white LEDs may be made up of light emitting semiconductor structures that emit non-white light as well as wavelength converting structures that make the non-white light appear white to the viewer. For example, a white LED may be formed from a blue light emitting semiconductor structure covered by a yellow emitting phosphor layer (i.e., the wavelength converting structure), and may be referred to as a phosphor-converted LED (pc-LED). Photons of blue light emitted by the light emitting semiconductor structure may either pass through the yellow emitting phosphor layer as blue photons or may be converted into yellow photons by the yellow emitting phosphor layer. The blue and yellow photons that are ultimately emitted out of the LED combine to make the light emitted from the LED appear white to the viewer.